tv Democracy Now LINKTV May 23, 2012 8:00am-9:00am PDT
satellite motion, yum, yum or yuck, yuck? i think you're gonna find yum, yum. yeah, yum, yum, okay? let's review something, gang. i'll put a ball here, a little spring gun and another ball here and as you know when i release this, both balls will fall at the same time. did i not demonstrate that to you? let's try it again. if at first, you don't succeed, why try again? no sense being a fool about it. here we go. and indeed they hit the ground at the same time. and the rule there is gravity doesn't take a holiday on moving objects. let's suppose i just dropped them, what would happen? no surprise, but do you know to some people, it's a surprise that they do hit at the same time when they're fired. now i'm going to pull it back further. still the same time? that's got to be level, gang. and watch. still the same time.
the time it takes to drop has to do with how high it is, not how fast it's going sideways. we learned that? and how far it's gonna fall down will depend on how longer time. does anyone remember the relationship for how far down will it fall as time goes by? can i give you that relationship right here? 5t2, remember that? so in one second, how far will an object fall if you drop it? 5 meters. 5 meters, it'll fall 5 meters down. if you threw it straight out, would it continue straight out or would it fall below the straight-out point? let's suppose, for example, you got in a tower. and let's suppose it's five meters tall, where you are right here and you've just dropped an object. how long it takes to hit the ground?
one second. let's suppose i instead throw the object. how long does it take to hit the ground? let's suppose i throw it faster sideways. how long does it take to hit the ground? one second, because what it's doing, it's falling beneath the straight line it would take if it didn't fall, isn't that right? and that vertical distance from here to here, that vertical distance, 5t2, so 1 second to fall 5 meters. let's suppose i threw it really, really fast, so fast that the curvature of the world played a role, a second or longer than a second? longer than a second. can you kinda see that? because let's suppose i talk about... here's my straight line. it might be 5 meters here, but here it's gonna keep getting more and more and more than 5 meters, so it'll be in the air for a longer time when you take earth's curvature to account,
because we live in a curved world, don't we? isn't the world curved like that? now if you had a cannon at the edge of the beach and you grazed it right out so it's grazing right against the water and you fire a cannonball. if there's no gravity, of course, it would just continue straight, straight, straight and pretty soon the water would be below it, yeah? do you know how far out you have to go on the planet we live on before there's a 5 meter drop? check your neighbor and see if you're sitting next to someone who happens to remember that fact from your reading or from previous lectures. how far out do you have to go along the earth to get a 5 meter drop? - can i have an answer? - 8 kilometers. - again. - 8 kilometers. 8 kilometers, that's right. if you go 8 kilometers straight out, you will be 5 meters further than the ground than you were over here.
so let me ask you a question, gang. if you fire that cannonball at a low speed, plop, splasharoony. you fire a little higher speed, splasharoony down here. how fast would you have to fire that cannonball, no splash? check the neighbor, see if the neighbor know. how many say it's 8 kilometers per second? can i have a show of hands? yeah, my people, my people. 8 kilometers per second will do it. 1 second later, if you're 8 kilometers away, you'll be just as far off the ground as you were here, 'cause don't forget this distance above to that straight line is a 5 meter drop, which tells us how satellites operate. newton talked about that years ago. newton says consider a mountain high enough to be, not above gravity, a lot of people think above gravity, no, no, no, no, to be above the drag of the atmosphere.
put a cannon on there and fire that cannonball and guess how fast it'll orbit. 8 kilometers per second... what you do is you orbit all the way around-- you're falling all the time, fall, fall, fall without ever hitting the ground. so that speed will put you in orbit. so next time you're watching the television set and you see they're gonna put some satellite into orbit, see the rocket go off. rocket climbing, climbing, climbing. pretty soon you'll see the rocket start to go sideways, right? should it? --better. what if just went... right back down, see? so it'll go up, gotta get up above the air drag and it's getting up, up, up and now it's gonna get level. and when it starts to get level, down below at mission control, they're pushing that thing up to guess how fast? past tense of eat, 8, okay? 8 kilometers per second and then they just throw the controls off and go home. no more control needed.
gotta get going sideways, 8 kilometers per second, it's gonna fall, ain't it? but the earth's got a curve and guess what matches up? the curve of the earth or the curve of the fall, hey, hey, hey, it's what falls around and around. hey, hey, we got that, yeah? so satellites are all the time falling. how come the speed, 8 kilometers per second, how come the speed at all these points is the same? did you know what it is? if it's going 8 kilometers per second here, it's going 8 kilometers per second here, here, here, here, the speed stays the same. the speed doesn't change, so once they boost it up to 8, it will coast at that one speed, which begs the question... hc, how come? someone say because gravity ain't pulling on it up there. what do you say about that?
uh-uh, honey, if gravity ain't pulling on it, what's it gonna do? straight line off into space. gravity is pulling on it, just about as hard as down here. so how come gravity don't speed it up? got a bowling ball here, gang. any gravity pulling on the bowling ball? any gravity pulling on the bowling ball now? how many say, no there's no gravity pulling on it when it moves? stand up. we know gravity pulling on that, yeah? how come the gravity don't speed it up? it's moving upwards down. yeah, yeah, yeah. gravity pulling straight down, straight down. let me show you.
gravity pulling straight down. is there any component of that force along this direction? no, no, if gravity was kinda pulling at an angle like that, guess which way it would accelerating when i let go? it would start accelerating that way, see that? i mean, let's suppose, like this was a hill. and now gravity is pulling on it. does this force here have any component along the tabletop? answer end with a 'p', begin with a 'y' and the answer is yup, it do. it's kinda pulling down here. in fact, there's a way to do that where you kinda take the little rectangle. you guys been into vectors? and this component here, makes it accelerate down the incline. this component doesn't do any work anywhere, doesn't help it along, just holds it against the table, but this component, now it'll pick up. but when you put it on a level,
is there any component kinda this way, kinda this way? only down, so what? it's pulling sideways all the time? so when you're bowling and you let go of the ball, you can tell why it's rolling at constant velocity, because there's no force pointing that way or we say no component of force pointing that way. are you getting the component, i mean, the part, that's pulling straight down. is there anything out this way, that--no, no, no. down, that's it. on a hill, yeah. so if we put a big bowling ball, i mean a big bowling alley around the world, what would we get? here's the world and let's suppose we put a bowling alley up in the sky. we'll put it up in the sky to get away from the air drag, about 50 miles up, yeah? here, we kinda get a support there so it doesn't fall down, big structure. this is first class bowling man, okay? now you take that bowling ball and you roll it. when it's here, the force of gravity acting like that.
when it gets over here, force of gravity acting like that. is that down? you're onto that and some people think down's always this way. come on put yourself in a frame of reference of the world, get a cosmic view, yeah? how about here? which way is down, gang? australians know. like that, okay? and everywhere here, note how the force is pulling, always perpendicular and if it's pulling perpendicular, then there's no component along the alley. so once you've got it rolling, how is it gonna roll? steady, steady, steady, unless you mess with it, okay? so let's suppose i get it rolling in a certain speed and let's suppose i cut part of the alleyway here, play a trick on it. here it comes, i'm rolling it, maybe like 4 kilometers per second, that's pretty fast. here we go. later on, come to the edgeway, crash into the ground. roll it faster.
crash into the ground over there. roll it faster. boom, still crash into the ground. i wonder if there'd be a speed you could move it such that it would clear the gap. how many say, oh, no, there's no way to clear that gap? stand up, go on. see if you're sitting next to someone who can calculate in their mind, the reason in their mind or come up with the answer, how fast it gotta go to clear the gap? what'd be the answer, gang? past tense of eat... 8, 8 kilometers per second, you're gonna clear the gap. how about if you make the gap this big? gonna clear that gap? how about you make the alley this big? here's the alley, now here's your gap, get it going 8 kilometers per second, what are you gonna do? you're gonna clear the gap, you come right back again. take it away and send it-- so it keeps moving at steady speed
because it's always being pulled sideways to the way it's moving, yeah? have we got that? someone asks you, how come the satellites keep going the same speed, oh, maybe there's a rocket pushing it all the time. what do you guys say? uh-uh, it's coastin'. it must be coasting where there's no gravity. uh-uh, there is gravity. why don't gravity speed it up? if i take that object and let go, gravity speeds it up. why doesn't it speed up the satellite? well, that's the characteristic of satellite motion, honey, that's just the way it is, no reason for that. what do you guys say? because, why? 'cause it's moving, but gravity pulling sideways and so instead of moving out here, it moves to here. but then it's pulling sideways again, so it's always being pulled sideways. if you understand these things, if you do, then you can answer this question. i fire the cannonball at 8 kilometers per second, how fast is it going here? 8 kilometers. - how fast here? - 8 kilometers. now i fired it 4 kilometers per second, 4.
smashes into the ground, it left the cannon at 4, it smashed into the ground at more than 4, no, no, no, no, no, less than 4, no, no, no, no, 4 exactly, no, no, no, no, there's no way to say. take a pick. let me ask you a question. i take these car keys. i toss the car keys 4 feet per second like this and you're gonna catch them out there, okay? they leave my hand 4 feet per second. i'm at the top of the mountain, you're down below. how many say, oh, you only threw 'em at 4, i'll catch with my bare hand. honey, you got a normal hand. they're gonna speed up? why they gotta speed up? they're going with gravity. when you go with gravity, what gravity gonna do to you? pull you faster and faster and faster. so this cannonball over here, this cannonball is gonna gain speed,
'cause it's not goin' sideways to the gravity anymore, i mean, perpendicular, look when it's in here, it's being pulled like that, it's sort of like a little angle in front of there, so the speed changes. let's come back up to here. when i threw that rock up here, that ball, i threw with a speed, maybe like this. and when i got here, it's got a speed still like that and when it gets over here, it still has a speed like that. these speeds are all the same. that's the horizontal component. you know why these components are the same? because there's been no force this way. you were neglecting air drag, gang. but you know what? when it gets to here, it's kinda moving down a little bit, a nd over here, it's even moving down further. and when i combine this motion and this motion, what do i get? i get motion like that. and when i combine this and this, what do i get? i get motion like that
and so what happens is the speed, here's the speed, that's the hypotenuse of our little triangle in here gang. you guys would be knowing the hypotenuse is always greater than either side, yeah? so this speed keeps getting more and more, why? 'cause i'm going with gravity. gravity giving me a component this way here. you see, when i'm on this bowling alley, everywhere i'm going, my speed is exactly sideways along the alley, see? 'cause there's no component of force this way, so it stays the same. there's no component of force this way, so this part stays the same. how about this part? going with gravity, it picks up, it picks up. and so what happens over here? over here the speed is more here than it was up here, so if it's 4 here, this component is 4, but the sum over here makes this greater. so when you're going with gravity, you're gonna pick up speed, 'cause gravity gonna help you along. going down in an angle, there's a component of gravity along the direction of motion like rolling down the hill.
there's a force and what i do is i'm moving this way. i have a component of that force like that. that's a force component and that force component means i have what that goes this way? begin with 'a'. acceleration that way. and if i get an acceleration that way, what do i have in terms of speed, what kind of speed? an ever-changing speed, that's acceleration is, yeah? so it picks up speed. so over here, a lot of people don't see this, over here, it picks up speed as it falls, but it doesn't pick up speed when it falls like that. do you guys see that? if you're understanding these ideas, maybe you are, maybe aren't, you can answer this question, which leads into the next aspect of everything we're talking about here. let's suppose instead of firing at 8 kilometers per second, it's gonna put it in circular orbit and by the way, that's only in closed orbit. out here, it turns out the speed is less and less, gravity is weaker,
but for closed orbit it's 8 kilometers per second. the moon is not moving 8 kilometers per second. it's moving much slower than that, it's way out there. this satellite here whips around in 90 minutes, yeah? how long does it take the moon to whip around? about 28, we call it a month, about 28 days, yeah, okay. let's suppose i fire my cannonball not at 8, not at 4, at 9, 9 kilometers per second. that's like over 20,000 miles per hour by the way. if i fired it 9 kilometers per second, ain't it gonna overshoot? it's not gonna follow here, is it? it's gonna overshoot, yeah? and when it gets out here, i gotta question for you. i fired it at 9, i wanna know if you know enough what's going on to be able to say with some certainty whether it's going 9, more than 9, less than 9
or say, you know i don't really be knowing. it's not *that i'd be annoyed, i don't really be knowing how to think about it and that's now one here, yeah? check the neighbor, more than 9, 9 or less than 9 when it gets to here? more than 9. the question is wouldn't the rotation of the earth affect all this? the answer is yes. guess what we ain't gonna count right now? in fact, let me tell you something about the rotation of the earth, okay? the earth's turning all the time, yeah? let's see, how does it turn? so the sun comes out, the sunlight-- let's see, go this way, oh, i get mixed up. which way does the earth turns, gang? it turns this way? yeah, it turns that way, okay. which part of the earth is moving faster in kilometers per second? up here or down here? if i hold it towards you like that, which part of that earth is traveling faster, gang? we talked about these ideas, near the equator.
guess why they launch from cape canaveral instead of nova scotia? guess why they get their eyes on the big island of hawaii for future launch? why do you suppose they're looking at hawaii for future launch? that 8 kilometers per second translates to 18,000 miles per hour. it turns out hawaii is going about 1,000 miles per hour. up here, going slower, so you know what you get? you get a free boost. so if you launch near the equator, you don't have to fire it off at 18,000. fire it off at 17,000, save you some fuel. so yes, the spin of the earth is a factor. so far i'm neglecting it and i neglect a lot of things in my course because i want you to see the base parts and then you can put the little embellishments on later. so in answer to that question when the satellite-- we went to another satellite yet, huh? when the projectile gets out here, 9, less than 9, more than 9, how many people say less than 9?
ooh, how many say no, exactly 9, it'll always stay the same, i learned that over here? how many say, well, i'm a free spirit, i say more than 9, 'cause it's going against gravity and gravity gonna kinda push it out there? now wait a minute, wait a minute, it's going against gravity, gravity gonna push it out, oh, wait a minute, no, no, if it's going against gravity, oh, i think it's less than 9. how many of you saying that? just like if i take this thing and throw it up in the air, when it leaves my hand, let's suppose it leaves at 9 feet per second, anyone know if it's gonna be more or less than 9 feet per second when it gets up here? common sense, come on, gonna be less, going against gravity. ain't that going against gravity? up here, gravity is pulling it to the center of the world. gravity pulling it like that. now look at this. it's moving like that. there's part of that gravity going against. this part here, gonna change course,
so it won't end up over here. it'll end down here. so you're going against a component of gravity and when you go against the component of gravity, it gonna slow you down. and so this thing gonna get slower. let's look at it over here. now it doesn't keep spiraling-- for ever 'cause it slows down, slows down and right over here, it's going sideways again so that maybe now it's only going 3 kilometers per second. it's been going up all the time and now what goes up... does it bother you when i say up? what goes up comes...down like that. and what it'll do is slow, slow, slow, fast, fast, fast. let me do this so-- how many australians here? okay, watch this. this might be satisfying to most of us. let's go like this...
kepler, johannes kepler never comprehended why it was that the planets been going around the sun in their elliptical paths. he never comprehended why it was they went so slow out here and so fast down here, he made the law, he discovered it. he discovered how much fast-- never had a model for thinking that allowed him to answer the question. when we look at the thing, a satellite, as simply a projectile interacting with the world, doesn't it make sense, when you throw it up, it's gonna slow down and finally come back again? honey, you put the landscape here and throw a rock up in the air. if some one had said to kepler, kepler, watch this, honey. take a rock. is it any mystery why it's going slower and then gain speed? it's just the responding to the gravity, yeah? and kepler would go... kepler didn't have that model.
you know what kepler's hang-up was? kepler thought that if the planet is moving this way, there gotta be a force that way. yeah, the poor guy. he said if it's moving this way, where's the force? the force is right down here, i mean toward here, huh? and when it gets here? kepler thought there was a force like this and he wanted to know, gee, how come the force keeps getting bigger? how come the force down here's so big? poor guy, a product of his time. poor us, we're products of our time. what kinda ideas do we have now, that later on people will say... oh, honey, i can't help it, i'm 20th century type. we're all are a product of our time and now we know, hindsight, 20/20 vision. now we know that hey, the force doesn't act that way. that's the direction of the velocity. the force acts this way
and over here it's strong and over here it's in between. and there's always a force acting toward the center of the world between here and here, see? between here and here, between here and here. and the force is always acting like that, see? and that's why it's going against the force going up, coming with the force, coming back down and that's why you get the different speeds, so simple. it's so simple if you get your head in the right frame. well, at its fastest point, would it still be 9 kilometers per second? no, it turns out the speed might be 9 down here if i choose that to be my model, 9 here, but then it'll keep getting less, less, less, less and some minimum speed up here, maybe 1. let's suppose this, maybe it gets to here. let's suppose it starts off at 9. this is a velocity vector now, not a force vector, force vector's-- here they're perpendicular, just at that point and right up here, but how about everywhere else? when i get up here, it might be 9, but over here, the force is pulling down.
i'm kinda going against this part. this part here, this component here, means later on, it won't be here. i'll be this way somewhere so it's like that, but this part here means you're going against that. it's gonna slow down, so over here it might be-- let me just guess, might be, might be 4. it's a guess, okay? maybe when it gets up here, it might be 2. and when it gets over here, guess what it gonna be? guess what it gonna be? 4. and what slowed it down, speeds it up, guess what it's gonna be down here. if it makes one trip, it's gonna make them all. that's why you get that thing off, it'll... indefinitely. kinetic energy, very, very big down here. kinetic energy, very small up here. oh, it looks like the conservation of energy-- - what kind? - potential. potential, over here, very, very close. it's got a little small potential on over here.
over here, very, very far, gotta big potential energy here. add these two up, you get a number, add these two up, you get a number. everybody in here know how this total number compared with this total number, right? 'ss' same, same. --ain't that neat? all along here, the total energy stays the same. yum? what happens when we hear that a russian satellite has crashed in australia or in canada, what really happens to the satellite? sometimes these satellites, they're falling all the time, by the way, but sometimes they fall and get closer. how come that happens? - air drag. - air drag. they drag their feet in the air. here's a satellite, i mean i say that not literally. here's satellite plowing through, okay? now it's way, way up there, maybe a couple of hundred miles high, no air drag. but maybe sometimes it's in kinda low orbit.
up here not too much drag but down here, you know what happened to the-- what was it? - skylab. - the skylab? skylab back in the 70s, it was in an elliptical orbit, okay, going around, around, around and what happened is there was a lot of solar activity and the atmosphere little bit deeper at times, and they thought, yeah, and this come in and hits a little bit of atmosphere. slows down a tiny, tiny bit, but once it slows down that means it's not gonna go so high next throw, huh? then it comes down, slow down a little bit more. next time up to here and so the orbit decays, because it drags its feet as it comes by and keeps decaying, decaying, decaying and then phoom, splasharoony. if you're going about 20,000 miles per hour and hit the air, guess what happens to you? okay, you get burned up, burned to a crisp. when you see the meteors up there, you know, you see the meteors like there was a meteor shower a few months ago.
you know what those meteors are? they call them falling stars, yeah? how big is a falling star on the average? humungous, humungous, humungous or humungous, humungous, humungous, humungous or about the size of a grain of sand. take your pick, gang. hint, last one. grain of sand, 15, 20 miles up and these things... even if they're standing still with respect to the sun, here comes the earth, thousands of miles an hour. and that grain of sand burns up in the air. and you look up, hey, wow, a star, honey. it ain't no star. it's a grain of sand, looks like-- if you lit a match up there, it'd look like a star and it's just a grain of sand burning up by friction, going so fast. and so when the space shuttle comes in, one of the big problems of the space shuttle when they first got this thing, how are you gonna get that thing back down into the air? you kinda go out gradual, gradual, gradual, but when you come back in, you're gonna come in with a splash, so they have to make it so it will melt, but the part that melts is not the part where the people's feet are, okay?
and you put these tiled blocks in the bottom. you gotta--the tile looks right thickness, right? so it melt away, melt away, melt away and finally, when it finally slow down, okay? you've got enough left over so that the part just left over is you. but that was a big problem getting with-- how do you enter the air at 18,000 miles per hour. that's a lot of friction gang, a lot of friction, burn you up. but these problems have been solved and we live at a time now where it's routine. interesting things about the elliptical path. this circle is an elliptical path and remember we talked about an ellipse? an ellipse is an oval-shaped type thing with a focus here and a focus here, remember that? and for the case of satellite motion, one focus is the planet itself and the other focus is just in space and around it goes. maybe a higher speed will put this focus over here
or further down and further down, okay? over here, even a circular orbit is an ellipse and if i go at a higher speed, now the focus--instead of having both foci together, the bottom focus is maybe right here. these foci will move as my friend ted bredstrom just told me a while ago, just got some illumination from my tas that that focus, these foci here just move along this dotted line and the faster you go, the more this focus here goes out, out, out, out, see? we're now, is we're down here, yeah? but here's an interesting thing too a lot of people don't know about. even up in here where you're just throwing it and it hit the ground. we all learned to call this a parabola, but you know what? it's a segment of an ellipse, because if that ground weren't there, it would go in an elliptical path with this focus, the center of the earth being the far focus and some nearer focus up here.
and if you throw it faster, okay? it'll follow a wider ellipse with this again the focus here and this one over here, closer in here. and as you get closer and closer to a circle, this keeps moving right down till they're both together and now you get the special case of a circle and beyond that, then this one here just kinda move down there. and so that parabolic path is part of an ellipse. if i fire it faster than 9, it'd shoot out like that, maybe that's 10, maybe that's 11 and at 11, it'll... see it up there, see it, see it, see it? guess how fast it comes by? 11. now i'm gonna fire it at 11.2. goodbye, bye-bye, honey. 11.2, ain't gonna come back.
11.2 gonna outrun gravitational pullback, it's gonna outrun it, gonna escape. that's the escape speed. go at 11.2 kilometers per sec, 25,000 miles an hour if you wanna translate it. go 25,000 miles an hour, goodbye, honey, you're gone. you don't come back to the earth. then you orbit around the sun. if i get way out in the edge of the solar system and i take a rock and i say, hey, earth, i see you down there, honey. and i take the rock and i, here we go. and that rock crashes into the earth by virtue of earth gravity. how fast did that rock hit? is there a upper limit? what's the fastest that rock gonna splatter into the ground?
let me tell you one of the neat things about being a teacher. i keep learning elementary physics a little bit more and more every year. if you had asked me that question several years ago, i would say, well, it would approach the speed of light and i didn't know what i was talking about, because the answer is much more elegant than the speed of light. let me give you a hint. if you're at the top of a building and i throw a rock as fast as i can to get to you and let's suppose i wanna escape the sky or something and you're at the top here and to escape the sky or something, i gotta throw at maybe 11.2 meters per second and it just gets to you and you catch it. that's how fast i gotta throw it to get it up there, all right? it's an easy question for you guys to answer when i say, if i take that rock and i just get up there and i drop it, hey, you catch it now, honey. how fast is it gonna be going when i catch it?
same, right? now i gotta question for you. the first question, you're out there beyond pluto. hey, earth, how are you doing down there, honey? you take a rock and you drop it. let it fall to earth by earth's gravity. get the sun out of the way, okay? just by earth's gravity. splat. i'll bet you're sitting next to someone who knows what the speed of the splat is, at least the upper speed, check it out. what's the maximum falling speed for planet earth? what's the answer, gang? 11.2 kilometers. 11.2 kilometers per second, right on. it's gonna be the same speed it takes to escape. how fast it has to go to get out there will be how fast it would fall back in again 'cause what slows it down-- hey, hey, hey, and it all ties together. are you ready for quiz that'll take care of all of mechanics? a little sample quiz, here we go. look over here, folks. here's a satellite going around in elliptical orbit
around the earth. i'm gonna ask you a bunch of questions and see if you can answer the questions. at what point a, b, c, d is the gravitational force that acts on that satellite a maximum? here, here, here or here? write on your paper a 'a,' a 'b,' a 'c,' or a 'd'. or if you think the gravitational force on the satellite is the same everywhere, then you write down a 'e.' same, same, right? nobody's gonna write down e for that one. in fact, what do we put down for an answer, gang? a, 'cause it's closer. b, huh? okay. number 2: at what point in the orbit does that satellite get the maximum speed? a, b, c, d or the same everywhere, e, it's an ellipse.
question number 3: at what point in orbit does that satellite have the maximum velocity? what, i got the maximum speed-- number 4: at what point in orbit does that satellite have the maximum kinetic energy? a, a, a. how many say, oh, probably where it's going slowest? come on, where's the maximum kinetic energy? - a. - huh, a? is it a? well, that means the maximum speed at 'a', all as? we like all as, yeah? number 5: where does that cast satellite have the maximum momentum? e. how many say, oh, it probably got the maximum amount where the earth's going slow? come on, nobody say that.
at what point in the sky does that satellite have the maximum potential energy? gravitational potential energy. off the as, honey, onto the what? - c. - c, huh? at what point in the sky does that satellite have the maximum total energy? that's potential and kinetic energy together. a? what would you use, gang, huh? a. at what point in orbit does that satellite have the maximum acceleration? maybe it's time to use the equation as a guide to thinking. maybe it'll have the maximum 'a' where it has the... will you be getting it?
can you handle these questions? if you can, you can be handling mechanics. can i give you the granddaddy? at what point in orbit does the satellite have the greatest angular momentum? that's the mass of the satellite times its speed times its radial distance from the earth. where is it maximum, a, b, c, d or e? think about that. you know what? that's physics. i'll catch you later.